In this lesson, we're going to look at all the different types of numbers. Now so far you've probably learned about whole numbers and fractions and maybe even decimals. But the higher up you go in algebra, you're going to learn that there's even more different types of numbers. This chart shows all the different types of numbers organized and how they're related to each other. In this lesson though, we're just going to look at the ones on the left side, all of the different real numbers. On the right side, you see that we also have imaginary numbers. I know that sounds kind of weird. How can you have imaginary numbers? Are they make believe ones that someone just made up like pretend numbers? Kind of, sort of. You're going to learn more about those once you start getting into more advanced algebra classes. First we're going to start at the bottom of the chart with the types of numbers that we first learn about very early on. These are the natural numbers. They're also called the counting numbers. When we count, we typically start with the number one and then go to two, three, four, etc. Next we have the whole numbers. The whole numbers include all of the natural counting numbers that we just talked about. But this time we also include the number zero. So we start with zero and then go on to one, two, three, etc. Next, we have integers. Integers include all of the whole numbers, so zero, one, and so on. But it also includes the negatives of those numbers. So if we take a look at this number line here, we can see that starting in the middle and going to the right, we have all of the whole numbers zero, and then one, two, three, and so on. To the left, we have the negatives of those numbers. So negative one, negative two, negative three. And the farther we move to the left, we get to more and more negative numbers. It's very important to remember that integers do not include fractions or decimals. This can be a very common mistake to make sometimes in algebra. So if you come across a fraction or a decimal, they are not integers. Next, we have the rational numbers, which include all of the integers that we just learned about. For example, the number negative 35 But it also includes the whole numbers and the natural numbers. Rational numbers can also include fractions and terminating decimals, which means that they are decimals that stop at a certain place value. So if we look at this number, we have 9.7563 and it stops at the three. So since it ends right there, we call it a terminating decimal. The other type of decimal is a repeating decimal. If we look at this example, we have six point twelve, but we also have a line or bar over the one and two. That means that those numbers keep repeating over and over and over for infinity. So when we see the bar over some of the numbers in the decimal, that means it's a repeating decimal and it still counts as a rational number. And lastly, we have the irrational numbers. Irrational numbers include non-terminating decimals. The word non-terminating means that they do not end, they don't stop. So if we look at this example 5.94571… then we have the dot, dot, dot after the one. That means that the number will keep going on and on and on forever. But since we don't have a bar over any of the numbers, it's not going to have a repeating pattern. So therefore it's not a repeating decimal But it is a non-terminating decimal because it will go on and on forever, just with no pattern. Another example is pi. And in math, we use this symbol to represent pi. But pi can also be written as a non-terminating decimal. Pi starts off as 3.14 and it keeps going on and on and on. The numbers never end and that makes it a non-terminating decimal. And all of those numbers are considered real numbers - all of the rational numbers, all of the fractions and decimals that we just looked at, all the whole numbers and integers. Also, all real numbers can be plotted on a number line. They all have a place, a position on the number line. So there we go. We just learned about all the different types of real numbers that are used in algebra.